Uncertainty relations and fluctuation theorems for Bayes nets

TL;DR

This paper develops fluctuation theorems and uncertainty relations for entropy production in complex systems modeled as Bayes nets, advancing stochastic thermodynamics for interconnected systems.

Contribution

It introduces fluctuation theorems and thermodynamic uncertainty relations specifically for systems represented by Bayes nets, including conditional theorems based on subsets of systems.

Findings

Derived fluctuation theorems for entropy production in Bayes nets

Established conditional fluctuation theorems for subsets of systems

Formulated thermodynamic uncertainty relations linking entropy production and current precision

Abstract

Recent research has considered the stochastic thermodynamics of multiple interacting systems, representing the overall system as a Bayes net. I derive fluctuation theorems governing the entropy production (EP)of arbitrary sets of the systems in such a Bayes net. I also derive ``conditional'' fluctuation theorems, governing the distribution of EP in one set of systems conditioned on the EP of a different set of systems. I then derive thermodynamic uncertainty relations relating the EP of the overall system to the precisions of probability currents within the individual systems.